The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent the work is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.
Polar codes are a class of error correcting codes, and can be employed to achieve the capacity of various communication channels. Construction of polar codes relies on a specific recursive encoding procedure. The recursive encoding procedure synthesizes a set of virtual channels from a plurality of usages of a transmission channel. The synthesized virtual channels tend to become either noiseless or completely noisy when the code length goes to infinity. This phenomenon is known as channel polarization. In their original construction, polar codes only allow code lengths that are powers of two. Puncturing techniques can be employed to modify polar codes in order to achieve any code length. In puncturing, one or more coded bits are selected and not transmitted.